Abstract
We propose a way of making graphene superconductive by putting on
it small superconductive islands which cover a tiny fraction of graphene
area. We show that the critical temperature, Tc, can reach several Kelvins
at the experimentally accessible range of parameters.
At low temperatures, , and zero magnetic field,
the density of states is characterized by a small gap
resulting from the collective proximity effect.
Transverse magnetic field is expected to destroy
the spectral gap driving graphene layer to a
kind of a superconductive glass state.
Melting of the glass state into a metal occurs
at a higher field Hg2(T).